0
votes
0answers
22 views

On modular group and quadratic forms

Let $\Gamma$ be the modular group, is the group of linear transformations of the upper half of the complex plane. Let $\mathbb Q_{N^2{d_K}}/\Gamma$ (the group of positive definite primitive quadratic ...
2
votes
1answer
71 views

A problem about the discrete logarithm

suppose there are a multiplicative cyclic group $F_p^*(p \;is\;big\; prime)$, and $G=\langle g \rangle(g \;is\; a\; generator)$ is a subgroup of it and $G$'s order is $q(q\;is\;big\;prime \;and ...
3
votes
1answer
114 views

Center of SO(V,q)

Let $V$ be finite dimensional vector spaces and $q$ is quadratic form. I'm looking for $Z(SO(V,q))$. where $SO(V,q)$ is special orthogonal group. If $\operatorname{dim} V$ is odd then ...
0
votes
1answer
72 views

Action of $SL_2(Z)$ on Markoff quadratic forms

My setting is as follows: Fix a Markoff form $f_m(x,y)$ (see definition in the link below). If $f_m$ has the form ${\alpha}x^2+{\beta}xy+{\gamma}y^2$ then each element $A\in SL_2(Z)$ acts on $f_m$ in ...